Modelling divergence in Relational Concurrent Refinement

Data refinement in a state-based language such as Z is defined using a relational model in terms of the behaviour of abstract programs. Downward and upward simulation conditions form a sound and jointly complete methodology to verify relational data refinements. On the other hand, refinement in a process algebra takes a number of different forms depending on the exact notion of observation chosen, which can include the events a system is prepared to accept or refuse. In this paper we investigate how divergence can be modelled relationally, and in particular show how differing process algebraic interpretations of divergence can be embedded in a relational framework. In doing so we derive relational simulation conditions for process algebraic refinement incorporating divergence.